Do galaxies that are receding from us faster than the speed of light disappear from our observations? (Intermediate)

Is there any proof that space expands faster than the speed of light, such as the sudden disappearance of stars or galaxies? If that hypothesis is true, shouldn't there be some stars and galaxies near the cosmic horizon that are disappearing from our observations?

Currently, we are certain that we live in a universe that is expanding at an increasing rate. As you read this, the universe expands at about 70 kilometers per second per megaparsec. This means that a galaxy 1 megaparsec away from us is receding at about 70 km/s, another galaxy 2 megaparsecs away from us is receding at 140 km/s, and so on. This is Hubble's law. Following the same logic, one could do the math to compute how far a galaxy has to be in order to move away at the speed of light. It turns out, galaxies 4300 megaparsecs away from us recede faster than light. This distance defines the "Hubble sphere", an imaginary sphere centered at us, outside which everything recedes faster than the speed of light. Note that, since the universe expands at an accelerated rate, the Hubble sphere increases its radius as time goes by.

Can we see light coming from galaxies outside the Hubble sphere? Receiving light from a source moving faster than light might seem odd, but this is actually possible. Imagine a galaxy outside the Hubble sphere, which emits a light pulse towards Earth. The pulse tries to makes its way to us, but it is "dragged" away from Earth by a region of space receding faster than light. It looks like we will never receive this pulse -- but wait a sec! As the universe expands, the Hubble sphere gets bigger, too. Now, if the rate at which the Hubble sphere expands is larger than the net velocity at which the photon recedes from us, the pulse will eventually pass from a superluminal region into a region receding from us slower than the speed of light. Take a look at this video, which transforms these words into a cool animation. Of course, as long as the pulse is traveling a region receding from us at a velocity smaller than the speed of light, it will eventually reach us. The conclusion is that we still can observe galaxies receding faster than light! Put another way, the Hubble sphere is not the limit of our observable universe.

How can we tell the universe is expanding faster than the speed of light in the first place? The wavelength of a light pulse traveling the universe is stretched as space expands, so the light gets redder. (That is, its wavelength increases.) This so-called cosmological redshift is measured by astronomers, so distant galaxies can be labeled by their redshift. The higher redshift of a galaxy, the faster it is receding from us. For any plausible model of our expanding universe, there exists a relatively simple conversion to translate redshift into recessional velocity. Not surprising by now, some of the galaxies we have observed exhibit redshifts resulting in superluminal recessional velocities!

Finally, one should note that, in practice, a receding galaxy may "disappear" from our observations due to cosmological redshift. Light coming from the galaxy gets redder and redder, leaving the detectability range of our instrument (our eyes or even a radio telescope). In addition, the time between successive pulses will increase so much that the galaxy will fade out until it vanishes.

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